极大平面图的算术——几何指标  

The Arithmetic-geometric Index of Maximal Planar Graphs

作　　者：崔淑玉[1] 王维凡[2] 田贵贤 CUI Shuyu;WANG Weifan;TIAN Guixian(Xingzhi College,Zhejiang Normal University,Jinhua,Zhejiang,321004,P.R.China;Department of Mathematics,Zhejiang Normal University,Jinhua,Zhejiang,321004,P.R.China)

机构地区：[1]浙江师范大学行知学院,浙江金华321004 [2]浙江师范大学数学系,浙江金华321004

出　　处：《数学进展》2024年第1期81-90,共10页Advances in Mathematics（China）

基　　金：Supported by NSFC(Nos.11801521,11771402,12031018)。

摘　　要：给定一个具有点集V(G)={v_(1),v_(2),…,vn}和边集E(G)的图G,其算术—几何指标AG定义为■其中di表记G中点vi的度数.最近,该拓扑指标在化学图论中被引入并得到广泛研究.本文分别刻画了直径为2且最小度为4的n阶极大平面图中具有最大和最小AG-指标的极大平面图.For a given graph G with vertex set V(G)={v_(1),v_(2),…,v_n}and edge set E(G),its arithmetic-geometric index AG is defined as■where d_i denotes the degree of the vertex v_i of G.This topological index was recently introduced in chemical graph theory and some properties of AG-index have also been investigated extensively.In this paper,we characterize the maximal planar graphs of order n with diameter 2 and minimum degree 4,which attain the maximum AG-index and minimum AG-index,respectively.

关 键 词：算术—几何指标 极大平面图 直径2 极值图 

分 类 号：O157.5[理学—数学]